# Properties

 Label 369600.b Number of curves $4$ Conductor $369600$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.b1 369600b3 $$[0, -1, 0, -19493633, 32986555137]$$ $$200005594092187129/1027287538200$$ $$4207769756467200000000$$ $$$$ $$28311552$$ $$2.9952$$
369600.b2 369600b2 $$[0, -1, 0, -1893633, -119044863]$$ $$183337554283129/104587560000$$ $$428390645760000000000$$ $$[2, 2]$$ $$14155776$$ $$2.6487$$
369600.b3 369600b1 $$[0, -1, 0, -1381633, -623364863]$$ $$71210194441849/165580800$$ $$678218956800000000$$ $$$$ $$7077888$$ $$2.3021$$ $$\Gamma_0(N)$$-optimal
369600.b4 369600b4 $$[0, -1, 0, 7514367, -956356863]$$ $$11456208593737991/6725709375000$$ $$-27548505600000000000000$$ $$$$ $$28311552$$ $$2.9952$$

## Rank

sage: E.rank()

The elliptic curves in class 369600.b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 369600.b do not have complex multiplication.

## Modular form 369600.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} + q^{9} - q^{11} - 6 q^{13} - 6 q^{17} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 